Mesh2Mesh and Combo Map examples.

Also fixed plotting codes to show the plots by default.

SimPEG/Examples/Maps_ComboMaps.py

@@ -0,0 +1,62 @@
+from SimPEG import Mesh, Maps, np
+
+def run(plotIt=True):
+    """
+
+        Maps: ComboMaps
+        ===============
+
+        We will use an example where we want a 1D layered earth as
+        our model, but we want to map this to a 2D discretization to do our forward
+        modeling. We will also assume that we are working in log conductivity still,
+        so after the transformation we want to map to conductivity space.
+        To do this we will introduce the vertical 1D map (:class:`SimPEG.Maps.SurjectVertical1D`),
+        which does the first part of what we just described. The second part will be
+        done by the :class:`SimPEG.Maps.ExpMap` described above.
+
+        .. code-block:: python
+            :linenos:
+
+            M = Mesh.TensorMesh([7,5])
+            v1dMap = Maps.SurjectVertical1D(M)
+            expMap = Maps.ExpMap(M)
+            myMap = expMap * v1dMap
+            m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
+            sig = myMap * m
+
+        If you noticed, it was pretty easy to combine maps. What is even cooler is
+        that the derivatives also are made for you (if everything goes right).
+        Just to be sure that the derivative is correct, you should always run the test
+        on the mapping that you create.
+
+    """
+
+
+    M = Mesh.TensorMesh([7,5])
+    v1dMap = Maps.SurjectVertical1D(M)
+    expMap = Maps.ExpMap(M)
+    myMap = expMap * v1dMap
+    m = np.r_[0.2,1,0.1,2,2.9] # only 5 model parameters!
+    sig = myMap * m
+
+    if not plotIt: return
+
+    import matplotlib.pyplot as plt
+    figs, axs = plt.subplots(1,2)
+    axs[0].plot(m, M.vectorCCy, 'b-o')
+    axs[0].set_title('Model')
+    axs[0].set_ylabel('Depth, y')
+    axs[0].set_xlabel('Value, $m_i$')
+    axs[0].set_xlim(0,3)
+    axs[0].set_ylim(0,1)
+    clbar = plt.colorbar(M.plotImage(sig,ax=axs[1],grid=True,gridOpts=dict(color='grey'))[0])
+    axs[1].set_title('Physical Property')
+    axs[1].set_ylabel('Depth, y')
+    clbar.set_label('$\sigma = \exp(\mathbf{P}m)$')
+    plt.tight_layout()
+    plt.show()
+
+
+if __name__ == '__main__':
+    run()
+